Mavis Borchard, principal of Borchard Investments, is discussing portfolio strategy with Wilford Tupper, a potential client who walked into her office in the hopes of finding a shrewd way to invest an $800,000 IRA roll-over. Tupper is an experienced investor with other stock holdings, but he does not have the time to manage his own account. After listening to Tupper's investment goals, Borchard suggests a policy of active management, listing several of its benefits. - "The potential returns of this strategy are higher than those of passive-management strategies, yet the risk-reward trade-off is appealing. The information ratio for active management is higher than the ratio for passive management."
- "My optimization approach limits risk by using a factor model that takes into account the covariance of different risk factors."
- "To ensure that my portfolios deliver the best performance and that I don't deviate from my original investment style, I regress my returns against three indexes, a large-cap, a mid-cap, and small-cap."
- "I use a bottom-up approach to select stocks, focusing most on industry conditions."
Tupper is not satisfied with Borchard's strategies and asks about other types of investments. Historically, Tupper has not been successful at beating the market with his large-cap stock choices, but he is a firm believer in reversion to the mean. Borchard then recommends an enhanced indexing strategy. She suggests that Tupper start with 60 percent of his money in a market index fund, then divide the remainder between two portfolio managers, one who manages accounts in a large-cap blend style, and one who buys small-cap stocks with a value slant. Borchard expects the risk-free return to remain at 4.3 percent for the rest of the year and projects a market return of 12.7 percent and market risk of 18.6 percent for the year. The following is some data on expectations for both investment managers. Assume the correlation between the equity manager's active returns are zero. | Manager | Expected Return | Expected Risk | | Large-cap blend manager | 13.8% | 27.5% | | Small-cap value manager | 17.5% | 30.1% |
This plan appeals to Tupper, but he is still not sure in what index he should invest. He is picky about his indexes and would like any selections to meet a number of criteria: - The index must be investable.
- Transaction costs must be low.
- The index value must be easy to track.
- Index construction must allow investors to mimic the index with minimal tracking risk.
- The index must reflect the broader market as closely as possible.
While Tupper likes the mix of index funds and active management proposed by Borchard, he is also concerned that the active managers stick to their knitting. Borchard generally uses a large-cap index like the Dow Jones Industrial Average as a benchmark, but Tupper wants a benchmark customized to each manager's investment style. Borchard reluctantly agrees to provide a customized benchmark. She generally uses returns-based analysis to track whether money managers stay on target, but Tupper prefers a holdings-based approach. To best meet Tupper's index requirements, Borchard should select: | A) | a price-weighted index. |
| B) | a capitalization-weighted index. |
| | C) | an equal-weighted index. |
| | D) | an index reconstituted by committee, rather than by rule. |
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Answer and Explanation
Borchard seeks an index that reflects the broader market as closely as possible. This suggests a price-weighted index is out, as nominal stock prices are somewhat arbitrary and quite changeable, so the index's complexion can change simply because of a stock split. Low transaction costs favor capitalization-weighted indexes rather than equal-weighted indexes that must be rebalanced more often. The investability requirement also weighs on equal-weighted indexes, which tend to favor smaller stocks, which in turn may offer less liquidity. That leaves a capitalization-weighted index. Most indexes are easy to track. Index reconstitution policies can affect tracking risk and transaction costs, but are not relevant to investability and how effectively an index reflects the market.
Which of Borchard's statements is likely to be most effective at convincing Tupper to let her actively manage his account? | A) | "My optimization approach limits risk by using a factor model that takes into account the covariance of different risk factors." |
| | B) | "To ensure that my portfolios deliver the best performance and that I don't deviate from my original investment style, I regress my returns against three indexes, a large-cap, a mid-cap, and small-cap." |
| C) | "The potential returns of this strategy are higher than those of passive-management strategies, yet the risk-reward trade-off is appealing. The information ratio for active management is higher than the ratio for passive management." |
| | D) | "I use a bottom-up approach to select stocks, focusing most on industry conditions." |
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Answer and Explanation
None of the arguments is particularly compelling, but at least the statement about the information ratio is true and relevant. Active management does have a higher information ratio than passive management. Optimization applies to passive or semiactive management, not active management. Regressing returns against cap-weighted indexes will not determine whether the fund emphasizes value or growth stocks, so it will not detect growth or value style drift. Bottom-up approaches depend little on industry conditions, relying mostly on the fundamentals of individual stocks.
Assuming a 30 percent weighting in large-cap stocks, Borchard's enhanced indexing strategy for Tupper should generate an active return closest to:
Answer and Explanation
The strategys active return represents the weighted average of the active returns of each component. To calculate the active return, subtract the expected market return from the expected returns of each strategy. The large-cap manager has an estimated 13.8% return. Subtract the projected 12.7% market return, and the active return is 1.1%. For the small-cap strategy, the active return is 4.8%. The index fund is expected to earn the market return of 12.7%, for an active return of 0%. 1.1% × 30% + 4.8% × 10% + 0% × 60% = 0.81%. Thats the strategys expected active return.
The strategys active return represents the weighted average of the active returns of each component. To calculate the active return, subtract the expected market return from the expected returns of each strategy. The large-cap manager has an estimated 13.8% return. Subtract the projected 12.7% market return, and the active return is 1.1%. For the small-cap strategy, the active return is 4.8%. The index fund is expected to earn the market return of 12.7%, for an active return of 0%. 1.1% × 30% + 4.8% × 10% + 0% × 60% = 0.81%. Thats the strategys expected active return. The strategys active return represents the weighted average of the active returns of each component. To calculate the active return, subtract the expected market return from the expected returns of each strategy. The large-cap manager has an estimated 13.8% return. Subtract the projected 12.7% market return, and the active return is 1.1%. For the small-cap strategy, the active return is 4.8%. The index fund is expected to earn the market return of 12.7%, for an active return of 0%. 1.1% × 30% + 4.8% × 10% + 0% × 60% = 0.81%. Thats the strategys expected active return.
Based on his belief in mean reversion, Tupper should pursue a strategy of: | | | | D) | market-cap blend investing. |
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Answer and Explanation
Tupper is a believer in mean reversion, which is a cornerstone of value investing. Momentum investors don't want mean reversion. Optimization is an indexing technique for which mean reversion is unimportant. As far as market-cap investing goes, reversion to the mean is no more or less important for one capitalization group relative to any other capitalization group.
Which of the following statements about holdings-based analysis is least accurate? It: | A) | can pick up style drift faster than returns-based analysis. |
| | B) | requires more individual judgment than returns-based analysis. |
| C) | requires the use of less data than returns-based analysis. |
| | D) | can yield different results depending on the method used. |
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Answer and Explanation
Holdings-based analysis requires more data than returns-based analysis. The other statements are true.
Assuming a 25 percent weighting in small-cap stocks, Borchard's enhanced indexing strategy for Tupper should generate active risk closest to:
Answer and Explanation
A portfolios active risk is the square root of the sums of the squares of the weighted average active risk. To calculate the active risk, subtract the expected market risk from the risk of each portfolio component. The large-cap strategys risk is 27.5%. Subtract the markets 18.6% risk, and you have active risk of 8.9%. The small-cap strategys active risk is 11.5%, and the index funds active risk is 0%, because the index tracks the market. Heres how to calculate the complete strategys active risk: Large-cap strategy: 8.9%2 × 15%2 = 0.0178%.
Small-cap strategy: 11.5%2 × 25%2 = 0.0827%.
Index fund: 0%2 × 60%2 = 0%. The sum of the squares is 0.1005%. The square root of 0.001005 is 3.17% and that is the portfolios active risk.
A portfolios active risk is the square root of the sums of the squares of the weighted average active risk. To calculate the active risk, subtract the expected market risk from the risk of each portfolio component. The large-cap strategys risk is 27.5%. Subtract the markets 18.6% risk, and you have active risk of 8.9%. The small-cap strategys active risk is 11.5%, and the index funds active risk is 0%, because the index tracks the market. Heres how to calculate the complete strategys active risk: Large-cap strategy: 8.9%2 × 15%2 = 0.0178%.
Small-cap strategy: 11.5%2 × 25%2 = 0.0827%.
Index fund: 0%2 × 60%2 = 0%. The sum of the squares is 0.1005%. The square root of 0.001005 is 3.17% and that is the portfolios active risk. A portfolios active risk is the square root of the sums of the squares of the weighted average active risk. To calculate the active risk, subtract the expected market risk from the risk of each portfolio component. The large-cap strategys risk is 27.5%. Subtract the markets 18.6% risk, and you have active risk of 8.9%. The small-cap strategys active risk is 11.5%, and the index funds active risk is 0%, because the index tracks the market. Heres how to calculate the complete strategys active risk: Large-cap strategy: 8.9%2 × 15%2 = 0.0178%.
Small-cap strategy: 11.5%2 × 25%2 = 0.0827%.
Index fund: 0%2 × 60%2 = 0%. The sum of the squares is 0.1005%. The square root of 0.001005 is 3.17% and that is the portfolios active risk. [此贴子已经被作者于2008-9-16 10:01:28编辑过] | 
发表于 2008-9-16 09:58
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